Area of a Quadrilateral

Q.

All the maths formulas for mensuration

Q. Question 4
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Q. Suppose that the radius r and area A = pi r square are differentiable function at t .write an equation that relates dA/st to dr/st

Q.

The diagonal of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field in $m^2$.

1. $210m^2$

2. $100m^2$

3. $234m^2$

4. $240m^2$

Q.

The length of the minute hand of a clock is 14 cm. Find the area in ${cm}^2$ swept by the minute hand in 5 minutes.

1. 51.3

2. 55.1

3. 60.2

4. 70.8

Q.

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m²).

1. 250

2. 300

3. 100

4. 200

Q.

Prove that for any quadrilateral in which the diagonals are perpendicular to each other, the area is half the product of the lengths of the diagonals.

Q.

In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field.

1. 2560
2. 2460
3. 3460
4. 2840

Q.

Find the area of the quadrilateral with diagonal $13m$and offsets $7m$ and $3m.$

Q.

In the trapezium PQRS shown below, PQ is parallel to RS. Find its area.

Q.

Find the area of the given quadrilateral ABCD. Given that the length of BD, AE and BC are 28 cm, 12 cm, and 8 cm respectively.

1. 300 $c{m}^2$

2. 280 $c{m}^2$

3. 340 $c{m}^2$

4. 320 $c{m}^2$

Q.

The diagonals of a quadrilateral are perpendicular to each other and their lengths are 16 centimetres and 10 centimetres. What is its area?

Q.

Area of a quadrilateral ABCD is $20c{m}^2$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is

1. 4 cm

2. 16 cm

3. 18 cm

4. 19 cm

Q. Find the area of the irregular polygon shaped fields given below.
(4 marks)

Q.

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 14m. Find the area of the field(in m²).

1. 275 square metres

2. 300 square metres

3. 100 square metres

4. 200 square metres

Q.

One diagonal of a quadrilateral is 35 centimetres long and the perpendiculars to it from the opposite vertices are 15 centimetres and 19 centimetres long. What is the area of this quadrilateral?

Q.

The figure ABCD is a quadrilateral in which AB is parallel and equal to CD and BC is parallel and equal to AD. Its area is

1. $72c{m}^2$

2. $36c{m}^2$

3. $24c{m}^2$

4. $64c{m}^2$

Q.

Question 62

The area of a rectangular field is $48m^2$ and one of its sides is 6m. How long will a lady take to cross the field diagonally at the rate of 20 m/min?

Q.

Find the area of quadrilateral ABCD in sq.units. Given AE = 5 units, BD =16 units and CF = 4 units

1. Data insuficient

2. 72 sq. units

3. 36 sq. units

4. 144 sq. units

Q.

A cow is tied with a rope of length $14m$ at the corner of a rectangular field of dimensions $20m\times 16m$. Find the area of the field in which the cow can graze.

Q.
HOPE is a square of perimeter 24 cm and T is the midpoint of side EP. PEN is an isosceles triangle where PN = EN = 5 cm. Find the area of triangle PEN.

1. 8 $c{m}^2$
2. 36 $c{m}^2$
3. 12 $c{m}^2$
4. 10 $c{m}^2$

Q.

Area of the following general quadrilateral is:

1. 

2. 

3. 

4. 

Q. 12. Calculate the area of quadrilateral ABCD is which a b equals to 32 centimetre AD Equal to 24 centimetre angle A equals to 90 degree and BC = CD = 52 centimetre

Q.

The area of a quadrilateral is 1470 square centimeters and the length of one of its diagonals is 42 centimetres. Calculate the sum of the lengths of the perpendiculars to this diagonal from the opposite vertices.

Q. The sides of a quadrilateral ABCD are 6cm, 8cm, 12cm and 14cm (taken inorder) respectively, and the angle between the first two sides is a right angle.Find its area.

Q. 41.the sides of a quadrilateral are 3, 4, 5 and 6cms. the sum of a pair of opposite angles is 120^° . show that the area of the quadrilateral is 3 root30 sq.cm.

Q. How will you measure the area of irregular shape?

Q.

The area of an isosceles trapezium is $34c{m}^2$ and the length of one of the parallel sides is 10 cm and Its height is 4 cm. Find the length of the other parallel side.

1. 4 cm.

2. 7 cm.

3. 9 cm.

4. 10 cm.

Q.

What will be the area A of the quadrilateral in each case with their diagonal $dcm$ & the sum of their heights $(h_1+h_2)cm$.

i) $d=20,(h_1+h_2)=10$

ii) $d=15,(h_1+h_2)=20$

iii) $d=20,(h_1+h_2)=25$

iv) $d=40,(h_1+h_2)=30$

Q.

The area of quadrilateral whose measurements are AC = 48 cm, BQ = 20 cm, DP = 10 cm is:

1. 780 cm²

2. 650 cm²

3. 720 cm²

4. 820 cm²